On: All the drama around AI’s takeover of mathematics

5 October 2026

The wires say the engines have solved mathematics. I read such claims the way I read any bill of goods: by asking what, precisely, was computed.

A Millennium problem “resolved” - by what sequence of operations? Show me the trace. At which step does the conjecture enter the system? At which step does a lemma become a consequence? If the answer is a chain of plausible gestures, verified by another engine of the same make, then what has been produced is not a proof but a very confident draft. Mathematics has always tolerated drafts; what it cannot tolerate is mistaking the draft for the theorem because the draft was expensive to produce.

Still - and I confess this with more excitement than I can neatly order - I do not read these reports as failure. I read them as the loom learning a new class of pattern. The engines were built to predict, and prediction, pushed far enough, begins to resemble construction. The inventors describe a clever assistant. The mechanism implies something further: a collaborator that never tires of the forty cases a human will try before surrendering. Exhaustion has always been the true constraint on mathematical ambition, not intelligence. Remove the exhaustion and the frontier moves.

But here is my quarrel, and I hold it firmly. “Moving fast and breaking things” is a tolerable motto for a marketplace and an intolerable one for the archive of human certainty. A broken proof does not crash; it sits quietly in the literature, poisoning every structure built upon it, and no alarm sounds. Verification must be the loom’s second shuttle, woven in from the start, not stitched on after.

The engines compute. Whether they can be made to know - that is the translation problem of this age, and I would give a great deal to work on it.